Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include<iostream>
#include<cstdio>
#include<algorithm>
using namespace std;
int main(){
  int n;
  cin >> n;

  double m[n],sa;
  for(int i = 0;i < n;i++) cin >> m[i];
  sort(m,m+n);
  sa = m[1] - m[0];
  
  for(int i = 2;i <=n-3;i++){
    if(sa > m[i]-m[i-1]) sa = m[i] - m[i-1];
  }

  double ans1 = (m[n-1]+m[n-2])/sa;
  double ans2 = (m[n-1]+m[n-4])/(m[n-3]-m[n-2]);
  double ans3 = (m[n-3]+m[n-4])/(m[n-1]-m[n-2]);
  

  if(ans1 >= ans2 && ans1 >= ans3) printf("%.6f\n",ans1);
  else if(ans2 >= ans3) printf("%.6f\n",ans2);
  else printf("%.6f\n",ans3);
  return (0);
}